96-573 Anton Bovier, Veronique Gayrard
AN ALMOST SURE CENTRAL LIMIT THEOREM FOR THE HOPFIELD MODEL (157K, PS) Nov 18, 96
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Abstract. We prove a central limit theorem for the finite dimensional marginals of the Gibbs distribution of the macroscopic overlap'-parameters in the Hopfield model in the case where the number of random patterns', $M$, as a function of the system size $N$ satisfies $\lim_{N\uparrow\infty} M(N)/N=0$, without any assumptions on the speed of convergence. The covariance matrix of the limiting gaussian distributions is diagonal and independent of the disorder for almost all realizations of the patterns.

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